SOLUTION: The arithmetic mean of six grades is 87. If the lowest grade is dropped, the mean is 89. What is the lowest grade?

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Question 1117373: The arithmetic mean of six grades is 87. If the lowest grade is dropped, the mean is 89. What is the lowest grade?
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Subtract the unknown test score (x) from the total of all 6 scores (87*6); that gives you the total of the other 5 scores (89*5):





The lowest score was 77.

Or here is another way to solve this kind of problem. If you understand it, it will get you to the answer faster than the formal algebraic method shown above.

When one score is dropped, the average of the other 5 scores increases from 87 to 89, an increase of 2.
The average increase of 2 on 5 test scores means there are 10 "additional" points total.
To keep things balanced, the score that was dropped had to have 10 "too few" points.
So the test score that was dropped was 10 points below the average, or 87-10 = 77.
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